Process for inhibiting the migration to the exterior of mineral oils consisting of saturated and/or aromatic hydrocarbons and/or of their volatile components, having from 10 to 25 carbon atoms included in packaging materials comprising recycled cellulosic fibres, characterized in that it comprises the operations of surface treatment of said packaging material to form a first polymer coating comprising an acrylic polymer, in contact with said fibres, and a second surface treatment by application of a second polymer coating comprising a cyclic olefin polymer on said first coating, where the total amount of acrylic polymer and of cyclic olefin polymer of the first and second coating is between 15 and 50 g/m2.